When Teone went outside, he saw the elderly couple's caravan begin to float away, and helped them to safety.
As he did so, he heard screams and saw another pair being swept away.
Mr Capper said his son had taken refuge in a flooded building with about 40 others.
Teone could hardly type on his phone because his hands were so cold.
He told his dad: "There's a lot of old people, a few injured, but people are still screaming out there, it's really dark and cold [and the] power's out."
Teone's caravan had been washed away with all of his belongings and he was left with only his wallet, passport and cellphone.
Peter Capper said last night: "At last contact, about 4.30pm, he was just running out of battery on his phone so I told him to turn it off and only use it for emergencies -- it's been probably four hours now.
"I am a bit worried, but the storm has moved along the coast towards Italy."
His son travelled to Antibes in July to get work on superyachts, after studying for a crewing certificate at Mahurangi Technical Institute in Warkworth. Mr Capper said that Teone, despite his light build, always put other people first, so he was not surprised to hear of his son helping people during the flood.
"He's a very determined, passionate kid when he puts his mind to something -- especially helping someone.
"I was very proud of him just for getting over there on his own steam and now he's saved people's lives too."
Mr Capper said his son was due to sign a 12-month superyacht contract in the next 24 hours, so would hopefully be fed, clothed and housed soon.
Late last night, his son was moved to an evacuation centre with about 200 others.
A Ministry of Foreign Affairs and Trade spokeswoman said the ministry was aware that a New Zealander was caught up in the flooding in France. Its embassy in Paris was monitoring the situation and was in contact with local authorities.
"The ministry is in contact with the individual's family and is offering consular advice."
Meanwhile, a woman in her 60s died in the resort city of Cannes when huge storms hit the region, sending water and debris coursing down submerged roads.
"Some cars were carried off into the sea," said Cannes Mayor Davis Lisnard, describing water levels halfway up car doors and trees uprooted on the city's main street. additional reporting AFP